Solve for x? Show the equation you used and your work.

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Answer 1 · 2017-01-18T09:31:59

$x=27$ .

Since the Ray $AD$ bisects the $/_BAC$ , we know from Geometry,

that, $(BD)/(DC)=(AB)/(AC) rArr 24/18=36/x rArr x={(18)(36)}/24=27$

Answer 2 · 2017-01-18T09:57:17

See below.

Using the so called sinus law

$Delta ABD->sin(angle(BAC)/2)/bar(BD)=sin(angleBDA)/bar(BA)$
$Delta ADC->sin(angle(BAC)/2)/bar(DC)=sin(angleADC)/x$

but $angleBDA+angleADC=pi$ so $sin(angleBDA)=sin(angleADC)$

Dividing the two relationships term to term we get

$bar(DC)/bar(BD)=x/bar(BA)$ so

$x = (bar(BA)bar(DC))/bar(BD)=(36 cdot 18)/24=27$